77edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 539467156 - Original comment: ** |
Wikispaces>Gedankenwelt **Imported revision 539554354 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-02-03 14:09:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>539554354</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span>= | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span>= | ||
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine]], the 31&46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto. | 77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine|valentine]], the 31&46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto. | ||
77et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]]. | 77et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]]. | ||
| Line 22: | Line 22: | ||
||> 4 ||> 62.338 ||= 28/27, 26/25 || | ||> 4 ||> 62.338 ||= 28/27, 26/25 || | ||
||> 5 ||> 77.922 ||= 21/20, 25/24 || | ||> 5 ||> 77.922 ||= 21/20, 25/24 || | ||
||> 6 ||> 93.506 ||= | ||> 6 ||> 93.506 ||= 135/128 || | ||
||> 7 ||> 109.091 ||= 16/15 || | ||> 7 ||> 109.091 ||= 16/15 || | ||
||> 8 ||> 124.675 ||= 15/14 || | ||> 8 ||> 124.675 ||= 15/14 || | ||
||> 9 ||> 140.260 ||= 13/12 || | ||> 9 ||> 140.260 ||= 13/12 || | ||
||> 10 ||> 155.844 ||= 12/11, 11/10 || | ||> 10 ||> 155.844 ||= 12/11, 11/10 || | ||
||> 11 ||> 171.429 ||= | ||> 11 ||> 171.429 ||= 72/65 || | ||
||> 12 ||> 187.013 ||= 10/9 || | ||> 12 ||> 187.013 ||= 10/9 || | ||
||> 13 ||> 202.597 ||= 9/8 || | ||> 13 ||> 202.597 ||= 9/8 || | ||
||> 14 ||> 218.182 ||= | ||> 14 ||> 218.182 ||= 256/225 || | ||
||> 15 ||> 233.766 ||= 8/7 || | ||> 15 ||> 233.766 ||= 8/7 || | ||
||> 16 ||> 249.351 ||= 15/13 || | ||> 16 ||> 249.351 ||= 15/13 || | ||
| Line 37: | Line 37: | ||
||> 19 ||> 296.104 ||= 32/27, 13/11 || | ||> 19 ||> 296.104 ||= 32/27, 13/11 || | ||
||> 20 ||> 311.688 ||= 6/5 || | ||> 20 ||> 311.688 ||= 6/5 || | ||
||> 21 ||> 327.273 ||= | ||> 21 ||> 327.273 ||= 98/81 || | ||
||> 22 ||> 342.857 ||= 11/9, 39/32 || | ||> 22 ||> 342.857 ||= 11/9, 39/32 || | ||
||> 23 ||> 358.442 ||= 16/13 || | ||> 23 ||> 358.442 ||= 16/13 || | ||
| Line 47: | Line 47: | ||
||> 29 ||> 451.948 ||= 13/10 || | ||> 29 ||> 451.948 ||= 13/10 || | ||
||> 30 ||> 467.532 ||= 21/16 || | ||> 30 ||> 467.532 ||= 21/16 || | ||
||> 31 ||> 483.117 ||= | ||> 31 ||> 483.117 ||= 120/91 || | ||
||> 32 ||> 498.701 ||= 4/3 || | ||> 32 ||> 498.701 ||= 4/3 || | ||
||> 33 ||> 514.286 ||= 27/20 || | ||> 33 ||> 514.286 ||= 27/20 || | ||
| Line 62: | Line 62: | ||
||> 44 ||> 685.714 ||= 40/27 || | ||> 44 ||> 685.714 ||= 40/27 || | ||
||> 45 ||> 701.299 ||= 3/2 || | ||> 45 ||> 701.299 ||= 3/2 || | ||
||> 46 ||> 716.883 ||= | ||> 46 ||> 716.883 ||= 91/60 || | ||
||> 47 ||> 732.468 ||= 32/21 || | ||> 47 ||> 732.468 ||= 32/21 || | ||
||> 48 ||> 748.052 ||= 20/13 || | ||> 48 ||> 748.052 ||= 20/13 || | ||
| Line 72: | Line 72: | ||
||> 54 ||> 841.558 ||= 13/8 || | ||> 54 ||> 841.558 ||= 13/8 || | ||
||> 55 ||> 857.143 ||= 18/11, 64/39 || | ||> 55 ||> 857.143 ||= 18/11, 64/39 || | ||
||> 56 ||> 872.727 ||= | ||> 56 ||> 872.727 ||= 81/49 || | ||
||> 57 ||> 888.312 ||= 5/3 || | ||> 57 ||> 888.312 ||= 5/3 || | ||
||> 58 ||> 903.896 ||= 27/16, 22/13 || | ||> 58 ||> 903.896 ||= 27/16, 22/13 || | ||
| Line 79: | Line 79: | ||
||> 61 ||> 950.649 ||= 26/15 || | ||> 61 ||> 950.649 ||= 26/15 || | ||
||> 62 ||> 966.234 ||= 7/4 || | ||> 62 ||> 966.234 ||= 7/4 || | ||
||> 63 ||> 981.818 ||= | ||> 63 ||> 981.818 ||= 225/128 || | ||
||> 64 ||> 997.403 ||= 16/9 || | ||> 64 ||> 997.403 ||= 16/9 || | ||
||> 65 ||> 1012.987 ||= 9/5 || | ||> 65 ||> 1012.987 ||= 9/5 || | ||
||> 66 ||> 1028.571 ||= | ||> 66 ||> 1028.571 ||= 65/36 || | ||
||> 67 ||> 1044.156 ||= 11/6, 20/11 || | ||> 67 ||> 1044.156 ||= 11/6, 20/11 || | ||
||> 68 ||> 1059.740 ||= 24/13 || | ||> 68 ||> 1059.740 ||= 24/13 || | ||
||> 69 ||> 1075.325 ||= 28/15 || | ||> 69 ||> 1075.325 ||= 28/15 || | ||
||> 70 ||> 1090.909 ||= 15/8 || | ||> 70 ||> 1090.909 ||= 15/8 || | ||
||> 71 ||> 1106.494 ||= | ||> 71 ||> 1106.494 ||= 256/135 || | ||
||> 72 ||> 1122.078 ||= 40/21, 48/25 || | ||> 72 ||> 1122.078 ||= 40/21, 48/25 || | ||
||> 73 ||> 1137.662 ||= 27/14, 25/13 || | ||> 73 ||> 1137.662 ||= 27/14, 25/13 || | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>77edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x77 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span></h1> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>77edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x77 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span></h1> | ||
<br /> | <br /> | ||
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 <a class="wiki_link" href="/cent">cent</a>s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and <a class="wiki_link" href="/7_4">7/4s</a> less flat than that, it represents an excellent tuning choice for both <a class="wiki_link" href="/Valentine"> | 77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 <a class="wiki_link" href="/cent">cent</a>s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and <a class="wiki_link" href="/7_4">7/4s</a> less flat than that, it represents an excellent tuning choice for both <a class="wiki_link" href="/Valentine">valentine</a>, the 31&amp;46 temperament, and <a class="wiki_link" href="/Starling%20temperaments">starling</a>, the 126/125 <a class="wiki_link" href="/planar%20temperament">planar temperament</a>, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as <a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit">11-limit starling</a> and <a class="wiki_link" href="/Starling%20family#Oxpecker">oxpecker</a> temperaments. It also gives the optimal patent val for various members of the <a class="wiki_link" href="/unicorn%20family">unicorn family</a>, with a <a class="wiki_link" href="/generator">generator</a> of 4\77 instead of the 5\77 which gives valentine. These are 7-limit <a class="wiki_link" href="/Unicorn%20family#Alicorn">alicorn</a> and 11- and 13-limit camahueto.<br /> | ||
<br /> | <br /> | ||
77et tempers out 32805/32768 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 126/125, 1029/1024 and 6144/6125 in the <a class="wiki_link" href="/7-limit">7-limit</a>, 121/120, 176/175, 385/384 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the <a class="wiki_link" href="/13-limit">13-limit</a>.<br /> | 77et tempers out 32805/32768 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 126/125, 1029/1024 and 6144/6125 in the <a class="wiki_link" href="/7-limit">7-limit</a>, 121/120, 176/175, 385/384 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the <a class="wiki_link" href="/13-limit">13-limit</a>.<br /> | ||
| Line 216: | Line 216: | ||
<td style="text-align: right;">93.506<br /> | <td style="text-align: right;">93.506<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">135/128<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 256: | Line 256: | ||
<td style="text-align: right;">171.429<br /> | <td style="text-align: right;">171.429<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">72/65<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 280: | Line 280: | ||
<td style="text-align: right;">218.182<br /> | <td style="text-align: right;">218.182<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">256/225<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 336: | Line 336: | ||
<td style="text-align: right;">327.273<br /> | <td style="text-align: right;">327.273<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">98/81<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 416: | Line 416: | ||
<td style="text-align: right;">483.117<br /> | <td style="text-align: right;">483.117<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">120/91<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 536: | Line 536: | ||
<td style="text-align: right;">716.883<br /> | <td style="text-align: right;">716.883<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">91/60<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 616: | Line 616: | ||
<td style="text-align: right;">872.727<br /> | <td style="text-align: right;">872.727<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">81/49<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 672: | Line 672: | ||
<td style="text-align: right;">981.818<br /> | <td style="text-align: right;">981.818<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">225/128<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 696: | Line 696: | ||
<td style="text-align: right;">1028.571<br /> | <td style="text-align: right;">1028.571<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">65/36<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: right;">1106.494<br /> | <td style="text-align: right;">1106.494<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">256/135<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||